A hard way to make things dark

A helium ion is at rest in a laboratory when it is put in an electric field of \( E = 2~\mbox{N/C}\). An infrared light, of wavelength \(2000~\mbox{nm}\), is directed towards the ion. The ion is moving towards the source of radiation. After what time in the laboratory frame in seconds will the ion absorb the infrared radiation?

Details and assumptions

The first absorption line of helium at rest occurs at a wavelength of \( \lambda_0 = 1083~\mbox{nm}\).

The mass of the helium atom (approximately the same as of the Helium ion) is \( 6.65 \times 10^{-27}~\mbox{kg}\).

Only one electron is taken from the helium atom to make it into an ion.

Neglect radiative losses due to acceleration.

You may neglect any relativistic effects in the acceleration of the ion, but not otherwise.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.